one-way ANOVA?

#1
Hi!
I was wondering if anyone could help me out. I want to compare the means of three groups. I hypothesize that there will be no significant difference in the means between two of the groups but a significant difference between these two groups and a third group. I thought this would be a one-way ANOVA but it does not show a significant difference between groups. However, if I do three separate t-tests I see the trend I was expecting. Considering I would have to adjust my alpha to account for the multiple tests (which would be fine, all tests were p<0.0001 but it is awfully sloppy) and thought this is a very simple comparison that I should be able to figure out, I was wondering if anyone could tell me what I'm doing wrong.
Thank you!! Happy holidays
 
#2
You have to do two different hypothesis tests. There is no easy way in mathematical statistics I think to write the test you speak of. You need to do 3 hypothesis tests: u1=u2, u1=u3, and u2=u3. It sounds like you've done them already.

Your other option is to do Ho: u1=u2=u3, Ha: At least two not equal If you do a combined test and they are considered equal, then that's that. However you should consider the pooled alpha of the test.